{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TSW7YHLUT2CHRBR34Y7KLB4RLY","short_pith_number":"pith:TSW7YHLU","canonical_record":{"source":{"id":"1907.09826","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-23T11:38:42Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a4594e33a752665d065b4f6ae0853ec4da1c0b19219c210ff2201936620930d8","abstract_canon_sha256":"3a1d29cf65e8e50c60a28adea20326b6ae7bf44b64041b9b98495c177a167e79"},"schema_version":"1.0"},"canonical_sha256":"9cadfc1d749e8478863be63ea587915e0ae287f716cbd9047b8c54defee4024a","source":{"kind":"arxiv","id":"1907.09826","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09826","created_at":"2026-05-17T23:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09826v1","created_at":"2026-05-17T23:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09826","created_at":"2026-05-17T23:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"TSW7YHLUT2CH","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TSW7YHLUT2CHRBR3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TSW7YHLU","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TSW7YHLUT2CHRBR34Y7KLB4RLY","target":"record","payload":{"canonical_record":{"source":{"id":"1907.09826","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-23T11:38:42Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a4594e33a752665d065b4f6ae0853ec4da1c0b19219c210ff2201936620930d8","abstract_canon_sha256":"3a1d29cf65e8e50c60a28adea20326b6ae7bf44b64041b9b98495c177a167e79"},"schema_version":"1.0"},"canonical_sha256":"9cadfc1d749e8478863be63ea587915e0ae287f716cbd9047b8c54defee4024a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:49.950689Z","signature_b64":"/WB+TJZL2frTMjKU3MMVWeU4iVHxSHfKNgKOguuH1i4Rs5Aoi6nOKa95GpArm5XJZwUV6GhBAPu+KIB3rBoTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cadfc1d749e8478863be63ea587915e0ae287f716cbd9047b8c54defee4024a","last_reissued_at":"2026-05-17T23:39:49.949945Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:49.949945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.09826","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pP78A3Qm6xAnmtP8dUyg7ggH4TndJbXQ0TpRo8N0yTDwgkYIKi3FWCoM6zThPdLifNxJy0tH9czYrRg3cBIpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:07:00.242634Z"},"content_sha256":"cb1735bc121d484839916f39bf39d2c847ccd009e34fe9c62695663c57bc6c3e","schema_version":"1.0","event_id":"sha256:cb1735bc121d484839916f39bf39d2c847ccd009e34fe9c62695663c57bc6c3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TSW7YHLUT2CHRBR34Y7KLB4RLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Antonio Masiello, Erasmo Caponio","submitted_at":"2019-07-23T11:38:42Z","abstract_excerpt":"We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers--Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not suitable for studying optimal regularity of the fundamental tensor, nevertheless, we obtain some partial results in this direction when the Finsler metric is Berwald."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09826","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VniJOoR42hhFIjgFFMZrHdY1PHekdW51LiFSQnl/llnoP/a02OYsAItG+d9NsLPHux68sxc6XEniJKkqcxaBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:07:00.242975Z"},"content_sha256":"cb782a103758327b3445d9b5793edbbb6faa744b39c8915ad893ca48930b0bbb","schema_version":"1.0","event_id":"sha256:cb782a103758327b3445d9b5793edbbb6faa744b39c8915ad893ca48930b0bbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY/bundle.json","state_url":"https://pith.science/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T18:07:00Z","links":{"resolver":"https://pith.science/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY","bundle":"https://pith.science/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY/bundle.json","state":"https://pith.science/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSW7YHLUT2CHRBR34Y7KLB4RLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TSW7YHLUT2CHRBR34Y7KLB4RLY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3a1d29cf65e8e50c60a28adea20326b6ae7bf44b64041b9b98495c177a167e79","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-23T11:38:42Z","title_canon_sha256":"a4594e33a752665d065b4f6ae0853ec4da1c0b19219c210ff2201936620930d8"},"schema_version":"1.0","source":{"id":"1907.09826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.09826","created_at":"2026-05-17T23:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"1907.09826v1","created_at":"2026-05-17T23:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09826","created_at":"2026-05-17T23:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"TSW7YHLUT2CH","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TSW7YHLUT2CHRBR3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TSW7YHLU","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:cb782a103758327b3445d9b5793edbbb6faa744b39c8915ad893ca48930b0bbb","target":"graph","created_at":"2026-05-17T23:39:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers--Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not suitable for studying optimal regularity of the fundamental tensor, nevertheless, we obtain some partial results in this direction when the Finsler metric is Berwald.","authors_text":"Antonio Masiello, Erasmo Caponio","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-23T11:38:42Z","title":"Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09826","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cb1735bc121d484839916f39bf39d2c847ccd009e34fe9c62695663c57bc6c3e","target":"record","created_at":"2026-05-17T23:39:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3a1d29cf65e8e50c60a28adea20326b6ae7bf44b64041b9b98495c177a167e79","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2019-07-23T11:38:42Z","title_canon_sha256":"a4594e33a752665d065b4f6ae0853ec4da1c0b19219c210ff2201936620930d8"},"schema_version":"1.0","source":{"id":"1907.09826","kind":"arxiv","version":1}},"canonical_sha256":"9cadfc1d749e8478863be63ea587915e0ae287f716cbd9047b8c54defee4024a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cadfc1d749e8478863be63ea587915e0ae287f716cbd9047b8c54defee4024a","first_computed_at":"2026-05-17T23:39:49.949945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:49.949945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/WB+TJZL2frTMjKU3MMVWeU4iVHxSHfKNgKOguuH1i4Rs5Aoi6nOKa95GpArm5XJZwUV6GhBAPu+KIB3rBoTAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:49.950689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.09826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb1735bc121d484839916f39bf39d2c847ccd009e34fe9c62695663c57bc6c3e","sha256:cb782a103758327b3445d9b5793edbbb6faa744b39c8915ad893ca48930b0bbb"],"state_sha256":"18a36194e8d8077287dd324b60ff52802fd19551e721841bd4a868fcb234af67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bafZrpNHvBG0bMd9O1hD/DfDL7DeQkxlytM13lTuc77EY31imdjXMafKaSz+KVA/Ju3AyFtQhRMLKcsR09blBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:07:00.245214Z","bundle_sha256":"35ea3cce04c9e1273ea1c81a8d12d7945a9799335db365179e776fa26fb2947e"}}